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caluc2-test2 Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

cirecles

x = h +- r*cos(t)
y = h -+ r*sin(t)
center = (h,k)
2t makes it go around twice
-t makes it go around backwards

rectangl

ArcLenth: L = root( 1 + f'(x)2 )
Suface of Revolu­tion:
X-axsis: S = root( 1 + f'(x)2 ) * 2 f(x)
Y-axsis: S = root( 1 + f'(x)2 ) * 2 x
Volum of Revolu­tion:
X-axsis: S = f(x)2
Y-axsis: S = x2

Parmetric

deriv:
dy/dx  ­  = y'/x'
dy2/dx2 = (dx/dy­)'/x'
ArcLenth: L = root( (dx/dt)2 + (dy/dt)2 )
(dx/dt)2 =
(dy/dt)2 =

convertoin

x = rsin
r = root( x2 + y2 )
y = rcso
= tan-1(y/x)

Polar

Area:  ­ ­ ­ ­  A = 1/2 (f())2
ArcLenth: L = root( (r)2 + (dr/d)2 )

conic

r = ed/(1+ecos)
r = ed/(1-ecos)
r = ed/(1+esin)
r = ed/(1-esin)
left  ­  | right
-----|­-------
down | up

r =

e
how you tell the type
d
deretix:
for cos x = d for sin y = d
 

centrodids

x̅ = 1/(f(x)-­g(x)) * x*[f(x­)-g(x)]
ȳ =1/(f(x)-­g(x)) * 1/2*[f(x)2-g(x)2]
if g(x) = x-axis you can just drop it

trig

 
/6
/4
/3
sin
1/2
root(2)/2
root(3)/2
cos
root(3)/2
root(2)/2
1/2
tan
root(3)/2
1
root(3)